TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.2 VL - 106 SP - 1 EP - 13 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization JF - Operations Research Forum N2 - Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91846 VL - 4 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning JF - Algorithms N2 - We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach. KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - https://doi.org/10.3390/a14010004 SN - 1438-0064 VL - 14 IS - 1 SP - 4 PB - MDPI ER - TY - JOUR A1 - Huynh, Ngoc A1 - Chegini, Fatemeh A1 - Pavarino, Luca A1 - Weiser, Martin A1 - Scacchi, Simone T1 - Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model JF - SIAM Journal on Scientific Computing N2 - A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters. Y1 - 2023 VL - 45 IS - 6 SP - A2836 EP - A2857 ER - TY - JOUR A1 - Ozel, Mehmet Neset A1 - Kulkarni, Abhishek A1 - Hasan, Amr A1 - Brummer, Josephine A1 - Moldenhauer, Marian A1 - Daumann, Ilsa-Maria A1 - Wolfenberg, Heike A1 - Dercksen, Vincent J. A1 - Kiral, Ferdi Ridvan A1 - Weiser, Martin A1 - Prohaska, Steffen A1 - von Kleist, Max A1 - Hiesinger, Peter Robin T1 - Serial synapse formation through filopodial competition for synaptic seeding factors JF - Developmental Cell N2 - Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses. Y1 - 2019 U6 - https://doi.org/10.1016/j.devcel.2019.06.014 VL - 50 IS - 4 SP - 447 EP - 461 ER - TY - JOUR A1 - Ranneberg, Maximilian A1 - Weiser, Martin A1 - Weihrauch, Mirko A1 - Budach, Volker A1 - Gellermann, Johanna A1 - Wust, Peter T1 - Regularized Antenna Profile Adaptation in Online Hyperthermia Treatment JF - Medical Physics Y1 - 2010 U6 - https://doi.org/10.1118/1.3488896 VL - 37 SP - 5382 EP - 5394 ER - TY - JOUR A1 - Schneck, Jakob A1 - Weiser, Martin A1 - Wende, Florian T1 - Impact of mixed precision and storage layout on additive Schwarz smoothers JF - Numerical Linear Algebra with Applications N2 - The growing discrepancy between CPU computing power and memory bandwidth drives more and more numerical algorithms into a bandwidth-bound regime. One example is the overlapping Schwarz smoother, a highly effective building block for iterative multigrid solution of elliptic equations with higher order finite elements. Two options of reducing the required memory bandwidth are sparsity exploiting storage layouts and representing matrix entries with reduced precision in floating point or fixed point format. We investigate the impact of several options on storage demand and contraction rate, both analytically in the context of subspace correction methods and numerically at an example of solid mechanics. Both perspectives agree on the favourite scheme: fixed point representation of Cholesky factors in nested dissection storage. Y1 - 2021 U6 - https://doi.org/10.1002/nla.2366 VL - 28 IS - 4 ER - TY - JOUR A1 - Schiela, Anton A1 - Stöcklein, Matthias A1 - Weiser, Martin T1 - A primal dual projection algorithm for efficient constraint preconditioning JF - SIAM Journal on Scientific Computing N2 - We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity. Y1 - 2021 U6 - https://doi.org/10.1137/20M1380739 VL - 43 IS - 6 SP - A4095 EP - A4120 ER - TY - JOUR A1 - Horenko, Illia A1 - Weiser, Martin A1 - Schmidt, Burkhard A1 - Schütte, Christof T1 - Fully Adaptive Propagation of the Quantum-Classical Liouville Equation JF - J. Chem. Phys. Y1 - 2004 UR - http://publications.imp.fu-berlin.de/65/ U6 - https://doi.org/10.1063/1.1691015 VL - 120 IS - 19 SP - 8913 EP - 8923 ER - TY - JOUR A1 - Subramaniam, Jayant S. A1 - Hubig, Michael A1 - Muggenthaler, Holger A1 - Schenkl, Sebastian A1 - Ullrich, Julia A1 - Pourtier, Grégroire A1 - Weiser, Martin A1 - Mall, Gita T1 - Sensitivity of temperature-based time since death estimation on measurement location JF - International Journal of Legal Medicine N2 - Rectal temperature measurement (RTM) from crime scenes is an important parameter for temperature-based time of death estimation (TDE). Various influential variables exist in TDE methods like the uncertainty in thermal and environmental parameters. Although RTM depends in particular on the location of measurement position, this relationship has never been investigated separately. The presented study fills this gap using Finite Element (FE) simulations of body cooling. A manually meshed coarse human FE model and an FE geometry model developed from the CT scan of a male corpse are used for TDE sensitivity analysis. The coarse model is considered with and without a support structure of moist soil. As there is no clear definition of ideal rectal temperature measurement location for TDE, possible variations in RTM location (RTML) are considered based on anatomy and forensic practice. The maximum variation of TDE caused by RTML changes is investigated via FE simulation. Moreover, the influence of ambient temperature, of FE model change and of the models positioning on a wet soil underground are also discussed. As a general outcome, we notice that maximum TDE deviations of up to ca. 2-3 h due to RTML deviations have to be expected. The direction of maximum influence of RTML change on TDE generally was on the line caudal to cranial. Y1 - 2023 U6 - https://doi.org/10.1007/s00414-023-03040-y VL - 137 SP - 1815 EP - 1837 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition. Y1 - 2023 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2023.3 VL - 115 SP - 3:1 EP - 3:6 ER - TY - JOUR A1 - Ullrich, Julia A1 - Weiser, Martin A1 - Subramaniam, Jayant A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita T1 - The impact of anatomy variation on temperature based time of death estimation JF - International Journal of Legal Medicine N2 - Temperature-based time of death estimation (TTDE) using simulation methods such as the finite element (FE) method promises higher accuracy and broader applicability in nonstandard cooling scenarios than established phenomenological methods. Their accuracy depends crucially on the simulation model to capture the actual situation. The model fidelity in turn hinges on the representation of the corpse’s anatomy in form of computational meshes as well as on the thermodynamic parameters. While inaccuracies in anatomy representation due to coarse mesh resolution are known to have a minor impact on the estimated time of death, the sensitivity with respect to larger differences in the anatomy has so far not been studied. We assess this sensitivity by comparing four independently generated and vastly different anatomical models in terms of the estimated time of death in an identical cooling scenario. In order to isolate the impact of shape variation, the models are scaled to a reference size, and the possible impact of measurement location variation is excluded explicitly, which gives a lower bound on the impact of anatomy on the estimated time of death. Y1 - 2023 U6 - https://doi.org/10.1007/s00414-023-03026-w VL - 137 SP - 1615 EP - 1627 ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Froehly, Algiane A1 - Huynh, Ngoc Mai Monica A1 - Pavarino, Luca A1 - Potse, Mark A1 - Scacchi, Simone A1 - Weiser, Martin T1 - Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution T2 - 10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023 N2 - The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes. Y1 - 2023 UR - https://www.scipedia.com/public/2023f U6 - https://doi.org/10.23967/c.coupled.2023.004 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Starý, Tomas A1 - Potse, Mark A1 - Weiser, Martin A1 - Loewe, Axel T1 - Electrograms in a Cardiac Cell-by-Cell Model N2 - Cardiac electrograms are an important tool to study the spread of excitation waves inside the heart, which in turn underlie muscle contraction. Electrograms can be used to analyse the dynamics of these waves, e.g. in fibrotic tissue. In computational models, these analyses can be done with greater detail than during minimally invasive in vivo procedures. Whilst homogenised models have been used to study electrogram genesis, such analyses have not yet been done in cellularly resolved models. Such high resolution may be required to develop a thorough understanding of the mechanisms behind abnormal excitation patterns leading to arrhythmias. In this study, we derived electrograms from an excitation propagation simulation in the Extracellular, Membrane, Intracellular (EMI) model, which represents these three domains explicitly in the mesh. We studied the effects of the microstructural excitation dynamics on electrogram genesis and morphology. We found that electrograms are sensitive to the myocyte alignment and connectivity, which translates into micro-fractionations in the electrograms. Y1 - 2024 ER - TY - JOUR A1 - Bartels, Tinko A1 - Fisikopoulos, Vissarion A1 - Weiser, Martin T1 - Fast Floating-Point Filters for Robust Predicates JF - BIT Numerical Mathematics N2 - Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations. Y1 - 2023 U6 - https://doi.org/10.1007/s10543-023-00975-x VL - 63 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Weiser, Martin ED - et al. Bristeau, M.-O. T1 - Local inexact Newton multilevel FEM for nonlinear elliptic problems T2 - Computational science for the 21st century Y1 - 1997 SP - 129 EP - 138 PB - Chichester: John Wiley & Sons. ER - TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Uram, Samuel A1 - Wolf, Sarah A1 - Conrad, Natasa Djurdjevac A1 - Weiser, Martin T1 - Multilevel Optimization for Policy Design with Agent-Based Epidemic Models JF - Computational Science N2 - Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples. Y1 - 2024 U6 - https://doi.org/10.1016/j.jocs.2024.102242 VL - 77 SP - 102242 ER - TY - CHAP A1 - Semler, Phillip A1 - Weiser, Martin T1 - Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems T2 - Proceedings of the MATH+ Thematic Einstein Semester on Mathematical Optimization for Machine Learning N2 - Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational budget. We address not only the choice of evaluation points but also of required simulation accuracy, both of values and gradients of the forward model. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs as well as a clear benefit of including gradient information into the surrogate training. Y1 - 2024 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Potse, Mark A1 - Loewe, Axel A1 - Weiser, Martin T1 - Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model T2 - 2023 Computing in Cardiology Conference (CinC) N2 - Conduction velocity in cardiac tissue is a crucial electrophysiological parameter for arrhythmia vulnerability. Pathologically reduced conduction velocity facilitates arrhythmogenesis because such conduction velocities decrease the wavelength with which re-entry may occur. Computational studies on CV and how it changes regionally in models at spatial scales multiple times larger than actual cardiac cells exist. However, microscopic conduction within cells and between them have been studied less in simulations. In this work, we study the relation of microscopic conduction patterns and clinically observable macroscopic conduction using an extracellular-membrane-intracellular model which represents cardiac tissue with these subdomains at subcellular resolution. By considering cell arrangement and non-uniform gap junction distribution, it yields anisotropic excitation propagation. This novel kind of model can for example be used to understand how discontinuous conduction on the microscopic level affects fractionation of electrograms in healthy and fibrotic tissue. Along the membrane of a cell, we observed a continuously propagating activation wavefront. When transitioning from one cell to the neighbouring one, jumps in local activation times occurred, which led to lower global conduction velocities than locally within each cell. Y1 - 2023 U6 - https://doi.org/10.22489/CinC.2023.385 SN - 2325-887X VL - 50 PB - Computing in Cardiology ER - TY - JOUR A1 - Semler, Phillip A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems JF - Inverse Problems N2 - In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures. Y1 - 2023 U6 - https://doi.org/10.1088/1361-6420/ad0028 VL - 39 IS - 12 SP - 125003 ER -